LONDON, June 2 (Reuters) - Greek shares fell on Tuesday on lingering uncertainty over the country’s debt problems, while a rebound in the euro -- whose weakness has boosted German exporters -- pushed investors out of German stocks towards southern European bourses.

Greece must repay four loans totalling 1.6 billion euros ($1.8 billion) to the International Monetary Fund this month, starting with a 300 million euro payment on June 5.

Failure to reach agreement this month could trigger a Greek default and lead to the imposition of capital controls and a potential exit from the euro zone.

The euro currency itself managed to shrug off the Greek worries, however, and rose following better-than-expected euro zone inflation numbers.

The euro’s rebound weighed on Germany’s DAX index, which hit record highs in April as the country’s exporters benefited from the euro’s general weakness so far this year, and pushed traders out of the DAX towards other markets.

While the DAX fell 0.7 percent, southern European stock markets seen as less sensitive to the euro’s exchange rate managed to rise, with the Italian, Spanish and Portuguese markets all up by around 1 percent.

“The rebound in the euro is much more of a negative for the DAX than the other southern European markets,” said Francois Savary, chief investment officer at Swiss bank Reyl.

PERNOD FALLS

The pan-European FTSEurofirst 300 index fell 0.8 percent, with French drinks group Pernod sliding 3.8 percent on concerns over the company’s margins.

Nevertheless, the FTSEurofirst 300 remains up by around 15 percent since the start of 2015.

The DAX is also up 16 percent since the start of the year, but is some 8 percent below its April record highs.

Most investors expect Greece to remain in the euro zone, and record low interest rates and other economic stimulus measures from the European Central Bank have enabled European stock markets to rally this year, despite the Greek uncertainty.

Goldman Sachs strategists also saw earnings growth as still supporting European equities, in spite of the Greek problems.

Today’s European research round-up (Additional reporting by Alasdair Pal and Francesco Canepa; Editing by Catherine Evans)